Estimates of p(L_R | M_⋆,  z) as a function of M_⋆ and L_R based on our maximum-likelihood fitting results for QGs. The colored dashed lines in the top and bottom rows represent our best-fit model from the unbinned maximum-likelihood fitting (see Equation 28 and Table 2) through combining data in the three fields (GOODS-N and COSMOS/UltraVISTA) over the entire redshift range (0.1 < z < 4) evaluated at the center of each redshift bin. The binned data points are scaled with the probability estimated by the model (see Equation 28) using the N_obs/N_mdl method of Aird et al. (2012) (see details in Section 6.3.3). In the top panel, the different colors represent different M_⋆ bins. In the bottom panel, the different colors indicate different L_R bins.